A320973 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = n^k * Product_{p|n, p prime} (1 + 1/p^k).
1, 1, 2, 1, 3, 2, 1, 5, 4, 2, 1, 9, 10, 6, 2, 1, 17, 28, 20, 6, 4, 1, 33, 82, 72, 26, 12, 2, 1, 65, 244, 272, 126, 50, 8, 2, 1, 129, 730, 1056, 626, 252, 50, 12, 2, 1, 257, 2188, 4160, 3126, 1394, 344, 80, 12, 4, 1, 513, 6562, 16512, 15626, 8052, 2402, 576, 90, 18, 2
Offset: 1
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 2, 3, 5, 9, 17, 33, ... 2, 4, 10, 28, 82, 244, ... 2, 6, 20, 72, 272, 1056, ... 2, 6, 26, 126, 626, 3126, ... 4, 12, 50, 252, 1394, 8052, ...
Links
- Wikipedia, Dedekind psi function
Crossrefs
Programs
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Mathematica
Table[Function[k, n^k Product[1 + Boole[PrimeQ[d]]/d^k, {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten Table[Function[k, SeriesCoefficient[Sum[MoebiusMu[j]^2 PolyLog[-k, x^j], {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten Table[Function[k, Sum[MoebiusMu[n/d]^2 d^k, {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
Formula
G.f. of column k: Sum_{j>=1} mu(j)^2*PolyLog(-k,x^j), where PolyLog() is the polylogarithm function.
A(n,k) = Sum_{d|n} mu(n/d)^2*d^k.